Pinching Theorems for Statistical Submanifolds in Sasaki-Like Statistical Space Forms
Keyword(s):
In this paper, we obtain the upper bounds for the normalized δ -Casorati curvatures and generalized normalized δ -Casorati curvatures for statistical submanifolds in Sasaki-like statistical manifolds with constant curvature. Further, we discuss the equality case of the inequalities. Moreover, we give the necessary and sufficient condition for a Sasaki-like statistical manifold to be η -Einstein. Finally, we provide the condition under which the metric of Sasaki-like statistical manifolds with constant curvature is a solution of vacuum Einstein field equations.
2014 ◽
Vol 2014
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pp. 1-6
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2016 ◽
Vol 26
(06)
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pp. 1750053
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1976 ◽
Vol 19
(3)
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pp. 381-386
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1985 ◽
Vol 8
(1)
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pp. 69-74
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2019 ◽
Vol 27
(3)
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pp. 97-112
2017 ◽
Vol 10
(04)
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pp. 1750067
2019 ◽
Vol 16
(08)
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pp. 1950129
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